Apparently similar neuronal dynamics may lead to different collective repertoire

TL;DR

This study compares two cellular automaton models of neuronal networks, revealing that similar local neuronal rules can lead to different collective behaviors depending on the network topology, emphasizing the importance of microscopic rules in large-scale brain simulations.

Contribution

It demonstrates how two models with similar local dynamics can produce distinct collective behaviors based on network topology, highlighting the significance of microscopic rules in neuronal modeling.

Findings

GH model exhibits various dynamical regimes including phase transitions.

KC model shows only a continuous phase transition.

Network topology influences collective dynamics differently in the two models.

Abstract

This report is concerned with the relevance of the microscopic rules, that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large scale neuronal networks. One model, due to Greenberg \& Hastings, (GH) can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi \& Copelli, (KC) represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the inter-neuronal interactions in large scale numerical simulations, in particular when the network topology is far from a mean field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.